Holger Siegel holgersiegel74 at yahoo.de
Tue Feb 22 22:31:12 CET 2011

```Am 22.02.2011 um 22:03 schrieb Alberto G. Corona:

> Recently I had to navigatate trough data structures chained with mutable referenes in th STM monad. The problem is that their values are enveloped in  Either or Maybe results.
>
> functional compositions in the Either of Maybe , or list  monads are not possible when the values are  embedded inside effect monads (i.e. STM or IO) . I tried  to find some trick to handle it.
>
> to summarize, given:
>
>  foo, :  a -> m (Maybe b)
>  bar :   b -> m (Maybe c)
>  baz :  c -> m (Maybe d)
>
> how to compose foo bar and baz? Or, at least,  Are something out there to handle it in the less painful way?.

fooBarBaz = runMaybeT (MaybeT . foo >=> MaybeT . bar >=> MaybeT . baz)

(untested)

>
> I solved the generalized problem  (chaining  any double monadic combination) with a sort of monadic connector that acts as a " double monadic" operator   >>>>==  so that
>
> return. return (x :: a) >>>>== foo >>>== bar >>>== baz
>
> can be possible. Although I don't know if  it is the best solution. I wonder why nobody has written about it before:
>
>  (>>>=)   ::  n a -> (a -> m(n b)) -> m(n b)
>
> (>>>>==) :: (Bimonad m n) => m (n a) -> (a -> m(n b)) -> m (n b)
> (>>>>==) x  f =  x >>= \y -> y >>>=  f
>
> x >>>> f = x >>>>== \ _-> f
>
> infixl 1 >>>>==, >>>>
>
> The instance for handling the Maybe monad under any other monad is very similar to the definition of the "normal" monad:
>
>    Just x  >>>= f = f x
>    Nothing >>>= _ = return \$ Nothing

Ignoring the newtype wrappers, this is the same as the actual monad instance of MaybeT:

newtype MaybeT m a = MaybeT { runMaybeT :: m (Maybe a) }